Abstract

We compute a light front wave function for heavy vector mesons based on long distance matrix elements constrained by decay width analyses in the Non Relativistic QCD framework. Our approach provides a systematic expansion of the wave function in quark velocity. The first relativistic correction included in our calculation is found to be significant, and crucial for a good description of the HERA exclusive $\mathrm{J}/\psi$ production data. When looking at cross section ratios between nuclear and proton targets, the wave function dependence does not cancel out exactly. In particular the fully non-relativistic limit is found not to be a reliable approximation even in this ratio. The important role of the Melosh rotation to express the rest frame wave function on the light front is illustrated.

Highlights

  • At large densities or small Bjorken-x, nonlinear QCD dynamics is expected to manifest itself in nuclear structure

  • The applied different phenomenological wave functions result in e.g., J=ψ production cross sections that differ up to ∼30% from each other [27,40,41]. This is a large model uncertainty, compared to the precise data that is already available from HERA and the LHC and especially given that the Electron Ion Collider (EIC) [42,43] is in the horizon

  • To reduce the model uncertainty related to the vector meson wave function, we propose in this work a new method to constrain the wave function for heavy mesons based on input from the nonrelativistic QCD (NRQCD) matrix elements

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Summary

INTRODUCTION

At large densities or small Bjorken-x, nonlinear QCD dynamics is expected to manifest itself in nuclear structure. The applied different phenomenological wave functions result in e.g., J=ψ production cross sections that differ up to ∼30% from each other [27,40,41] This is a large model uncertainty, compared to the precise data that is already available from HERA and the LHC and especially given that the Electron Ion Collider (EIC) [42,43] is in the horizon (and similar plans exist at CERN [44] and in China [45]). To reduce the model uncertainty related to the vector meson wave function, we propose in this work a new method to constrain the wave function for heavy mesons based on input from the nonrelativistic QCD (NRQCD) matrix elements These matrix elements capture nonperturbative long-distance physics and can be obtained by computing the vector meson decay widths in different channels as a systematic expansion in both the coupling constant αs and the quark velocity v.

Exclusive scattering
Virtual photon wave function
Dipole-target scattering
LIGHT CONE WAVE FUNCTION FROM NRQCD
Vector meson wave function in the rest frame
Overlap with photon
PHENOMENOLOGICAL WAVE FUNCTIONS
Boosted Gaussian
V jψ i: ð62Þ
Photon overlap
CONCLUSIONS
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